PhD position available at L2S, south of Paris

A PhD position is available at Laboratoire de Signaux et Systèmes (L2S), Gif sur Yvette, France. Please find details below. Do not hesitate to transfer this information to any colleague/student who might be interested.

Title: Control laws for innovative deep brain stimulation in the treatment of Parkinson disease: provable approaches based on optogenitics experimental data

Brief description: This Ph.D. thesis aims at adapting methodologies issued from control theory and dynamical systems to the field of neurosciences. The development of formal analytical results allows a better understanding of some neurological phenomena, and is a necessary requirement for the achievement of significant progresses in therapeutic treatments such as deep brain stimulation. Recent experimental and theoretical breakthroughs now make such analytical studies reasonable. In particular, this work will focus on neuronal synchrony, which is involved in many healthy brain functions but can also lead to pathological phenomena (such as Parkinson disease). The objective of this work is to develop new analysis and control methods, able to cope with the fundamentally complex behavior of neuronal populations (interconnection, heterogeneity, uncertainties, delays…). These methods will be inspired from related domains involving stability analysis of interconnected nonlinear systems, analysis of hybrid dynamics and robust control. More precisely, the Ph.D. thesis will comprise: the development a spike-rate model of the basal ganglia network based on experimental optogenetics data of healthy and parkinsonian primates, the confrontation of this model with a single-unit numerical model, the formal analysis of pathological oscillations onset based on the spike-rate model, and the development of realistic DBS control laws to alter these pathological oscillations.

Environment: The Ph.D. thesis will take place at Laboratoire des Signaux et Systèmes (L2S) – Supélec, South of Paris (France), in a team composed of applied mathematicians and control theoreticians. The acquisition of experimental data will be made in collaboration with Prof. Palfi’s team at Hospital Henri Mondor (Créteil, France).

Prerequisite: Although aiming at practical fallouts and relying on state-of-the-art experimental data, the contributions expected from this Ph.D. thesis are mostly of a theoretical nature. The candidate must have a background in applied mathematics, nonlinear/hybrid control theory, or computational neurosciences. Interests in interdisciplinary research are required. Skills in simulation software are desirable. Knowledge of French language is not required, but an appropriate level of English is necessary.